The “girih” tiles (from the Persian word meaning “knot”) are a set of five tiles that are used in various combinations to create Islamic geometric patterns for decoration of buildings in Islamic architecture. FIG. 1 shows a top view of the set (1) of five girih tiles in basic outline shape. The five shapes of the tiles are: a regular decagon (6) with ten interior angles of 144°; an elongated (irregular convex) hexagon (5) with interior angles of 72°, 144°, 144°, 72°, 144°, 144°; a bow tie (non-convex hexagon) (4) with interior angles of 72°, 72°, 216°, 72°, 72°, 216°; a regular pentagon (3) with five interior angles of 108°; and a rhombus (2) with interior angles of 72°, 108°, 72°, 108°. All sides of these tiles have the same length, and all of their angles are multiples of 36° (π/5 radians). All of the tiles, except the pentagon, have bilateral (reflection) symmetry through two perpendicular lines. Some tiles have additional symmetries; for example, the decagon has tenfold rotational symmetry (rotation by 36°), and the pentagon has fivefold rotational symmetry (rotation by 72°).
The girih tiles are each decorated with piece-wise straight lines that are typically painted on the tiles and that form a portion of a simulated weaving pattern, referred to as a “girih strapwork pattern.” FIG. 2 shows a top view of a set (7) of the five Girih tiles with their corresponding portions of the girih strapwork pattern. In particular, the respective pattern portions on the tiles include piece-wise straight lines that cross the boundaries of the tiles at the center of an edge at 54° (3π/10) to the edge, with two intersecting lines crossing each edge of a tile. FIG. 3 shows the five Girih tiles of FIG. 2 placed together to form an example of the strapwork pattern. FIG. 4 shows a larger and more extended example of a girih strapwork pattern formed by several tiles, including mostly the hexagon tile (5″) and the bow tie tile (4″), with a single decagon tile (6″) at the center.